2x - 3y = 7 and -3x + y = 7..multiply Equation 2 by THREE and add to Equation 1
-9x + 3y = 21...........................watch the y's disappear
-7x........ = 28
x = -4
substitute -4 instead of x in either of the ORIGINAL equations
2x - 3y = 7
2(-4) - 3y = 7
-8 -3y = 7..........add 8 to both sides
-3y = 15
y = -5
im not sure
Answer:
2/13 of an hour
Step-by-step explanation:
Answer:
31.76 ft and 58.64 ft
Step-by-step explanation:
The radius measures between 13 feet and 24 feet.
The wheel is able to turn 7π/9 radians before getting stuck.
We need to find the range of distances that the wheel could spin before getting stuck. That is, the length of arc.
Length of an arc is given as:
where θ = central angle = 7π/9 radians
r = radius of the circle
Therefore, for 13 feet:
For 24 feet:
The wheel could spin between 31.76 ft and 58.64 ft before getting stuck.
The product is 60.
We start out with the information we have. This forms a right triangle, with one leg being 24, the other leg x, and the hypotenuse 30. Using the Pythagorean theorem we have
x²+24²=30²
x²+576=900
Subtract 576 from both sides:
x²+576-576 = 900-576
x²=324
Take the square root of each side:
√x²=√324
x=18
We know that the formula for the volume of a triangular prism is V=(1/2bh)H, where b is the base of the triangle, h is the height of the triangle, and H is the height of the prism. Substituting our known information we have:
720=(1/2*18*24)y
720=216y
Divide both sides by 216:
720/216 = 216y/216
3 1/3 = y
This means the product of x and y would be:
18(3 1/3)
18(10/3)
180/3
60
The constants are 2, -10, and 5
the variables are x and y
